%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM565+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:01 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 14 unt; 5 def)
% Number of atoms : 156 ( 29 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 170 ( 62 ~; 48 |; 42 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,conjecture,
! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) )
=> ( ( ~ ? [W1] : aElementOf0(W1,slcrc0)
& aSet0(slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,negated_conjecture,
~ ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) )
=> ( ( ~ ? [W1] : aElementOf0(W1,slcrc0)
& aSet0(slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
fof(f99,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f106,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f107,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f202,plain,
! [W0] :
( ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f203,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( X0 = slcrc0
| sbrdtbr0(X0) != sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f341,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f342,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f374,plain,
xK = sz00,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f381,plain,
? [W0] :
( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& aSet0(slcrc0)
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f382,plain,
( sdtlpdtrp0(xc,sK23_skl) != sdtlpdtrp0(xc,slcrc0)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& aSet0(slcrc0)
& aElementOf0(sK23_skl,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(sK23_skl) = sz00
& aSubsetOf0(sK23_skl,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,sK23_skl) )
& aSet0(sK23_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(W0,sK23_skl)],[f381]) ).
fof(f385,plain,
aSubsetOf0(sK23_skl,xS),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f386,plain,
sbrdtbr0(sK23_skl) = sz00,
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f388,plain,
aSet0(slcrc0),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f390,plain,
sdtlpdtrp0(xc,sK23_skl) != sdtlpdtrp0(xc,slcrc0),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f509,plain,
( aSet0(sK23_skl)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f110,f385]) ).
fof(f510,definition,
( sQ0_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ0_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ1_spl
<=> aSet0(sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f509,f510,f513]) ).
fof(f517,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f342]) ).
fof(f518,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f521,plain,
sbrdtbr0(sK23_skl) = xK,
inference(backward_demodulation,[status(thm)],[f374,f386]) ).
fof(f543,definition,
( sQ5_spl
<=> sK23_skl = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ5_spl
| sK23_skl = slcrc0 ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f765,plain,
( ~ sQ5_spl
| sdtlpdtrp0(xc,sK23_skl) != sdtlpdtrp0(xc,sK23_skl) ),
inference(backward_demodulation,[status(thm)],[f544,f390]) ).
fof(f769,plain,
( ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f765]) ).
fof(f770,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f769]) ).
fof(f817,definition,
! [X0] :
( sQ46_spl
<=> ( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f818,plain,
! [X0] :
( ~ sQ46_spl
| ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f826,plain,
! [X0] :
( ~ sQ46_spl
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f818]) ).
fof(f827,plain,
( ~ sQ46_spl
| ~ isFinite0(slcrc0) ),
inference(resolution,[status(thm)],[f826,f388]) ).
fof(f835,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f827,f99]) ).
fof(f836,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f835]) ).
fof(f866,plain,
! [X0] :
( X0 = slcrc0
| sbrdtbr0(X0) != xK
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f374,f204]) ).
fof(f868,plain,
( sK23_skl = slcrc0
| ~ aSet0(sK23_skl) ),
inference(resolution,[status(thm)],[f866,f521]) ).
fof(f872,plain,
( sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f868,f513,f543]) ).
fof(f878,plain,
$false,
inference(sat_refutation,[status(thm)],[f516,f518,f770,f836,f872]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM565+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n026.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 02:42:53 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.45 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.56 % Elapsed time: 0.123262 seconds
% 0.23/0.56 % CPU time: 0.142249 seconds
% 0.23/0.56 % Total memory used: 14.350 MB
% 0.23/0.56 % Net memory used: 14.329 MB
%------------------------------------------------------------------------------